In numerous service and production branches there is the need to assign staff members in the framework of a deployment plan over a certain period of time to different jobs to be accomplished. To this end, traditionally deployment plans are created manually by means of experience values. For applications with a relatively high fraction of personnel costs and a temporary varying need of staff members, staff scheduling may be complicated; its optimization, however, may often lead to a considerable increase in productivity.
A typical context for the application of a staff scheduling system is a call center, at which a variable number of telephone calls arrives during the day which are answered by staff members divided into shifts. In many cases, call centers are a central connector in the relationship between a producer or service provider and a client. In some fields, such as direct banks and telecommunication service providers, call centers are, in fact, the only interface between the client and the company. Hence, many companies are interested in a client-orientated, and at the same time, efficient operation of their call centers, so that the management of call centers has become an application-orientated field of research in the realm of optimization. Thereby, the problem is essentially to conciliate the divergent aims to provide the client on the one hand with a quality of service that is as high as possible, and on the other hand to operate a call center in a cost-saving way.
A fundamental service quality parameter in the realm of call centers is for instance the accessibility, i.e. how quickly a client is connected to a staff member. In practice, it is frequently dealt with the quantity “telephone service factor” (TSF), which is composed of two components: a temporal target within which calls are to be answered by a staff member (for instance within 20 seconds) and a percentage of all calls, for which this target is achieved (for example 80 percent). In some call centers the average waiting time of the callers is used as a quantity to be measured in computing the accessibility. Telephone service factor and average waiting time, however, can be transformed into each other mathematically. A further parameter is, for example, the immediate solution rate, which expresses the percentage of all calls that are resolved in a first contact with the customer. A third parameter is the solution time, which indicates how long it takes until the customer is provided with a result.
The forecast of the number of telephone calls to be expected in a call center within a time interval—often denoted as working volume (number of telephone calls*average duration of a call/3600 seconds)—may be made by means of experience values, which are based on historical observations since the number of calls to be expected is subject to daily, weekly and seasonal cycles. The calculation of how many staff members are needed, in view of the predicted working volume, to achieve a certain quality of service can be performed using a formula which is common in the realm of call centers, the so-called Erlang C-formula (see Borst, S., and Seri, P., “Robust Algorithms for Sharing Agents with Multiple Skills,” Bell Labs, Lucent Technologies, Murray Hill, N.J., 2000, p. 5). However, this formula makes some assumptions which do not always apply in reality and often leads in practice to personnel overstaffing of the call center so that there have been further attempts to make a more accurate forecast with regard to the number of call center staff members needed by means of simulation programs. In particular the Erlang C-formula assumes that each staff member is only qualified for one type of query.
Since typically in a call center customers call with different requests the staff members in their entirety have to possess different qualifications in order to be able to cover the spectrum of customer queries as far as possible. While in some call centers the staff members are only qualified for one type of request, in other call centers the staff members are trained in such a way that they may respond to different types of requests. As will be explained more precisely later, it is useful if at least some of the staff members are able to answer different types of queries. In this context, the so-called “pooling effect,” which will be explained in more detail below, shows its impact. According to this effect a multiple qualification of staff members may lead to a better quality of service (cf. e.g. H. Henn et al., Handbuch Call Center Management, telepublic Verlag, Hannover, 2nd edition, p. 204-205 and Borst and Seri, p. 9, who express this effect as follows: “Potential economies of scale from dynamically sharing the agents among the various call classes”).
In the patent specification U.S. Pat. No. 6,044,355 of the company IEX Corp. a method for a temporary staff member scheduling in a working environment is presented, where individual staff members possess different qualifications and the requirement for staff members with different qualifications is subject to temporal fluctuations. The period of time to be simulated is divided into shorter time intervals and to every time interval a number of staff members—initially only estimated—with corresponding qualifications is assigned, and this number is adapted in the course of several passes of simulations by means of a feedback mechanism. Telephone calls are simulated according to the forecast call volume and how well the scheduled staff members, with their respective qualifications, handle the call volume is verified. The results of the simulation are evaluated statistically and are used to improve the assignment of staff members. After a series of simulation passes an assignment of staff members with the corresponding qualifications is found which achieves the desired quality of service.